Question

The eccentricity of the ellipse $9x^2+25y^2=225$ is

• A. $\frac{3}{4}$
• B. $\frac{4}{5}$
• C. $\frac{9}{16}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B $\frac{4}{5}$

$9x^2+25y^2=225\Rightarrow \frac{x^2}{5^2}+\frac{y^2}{3^2}=1\Rightarrow a=5,b=3\therefore \text{Eccentricity},e=\frac{\sqrt{a^2-b^2}}{a}=\frac{\sqrt{5^2-3^2}}{5}=\frac{4}{5}$